SSC CGL 20 Aug 2021 Shift 1 Paper

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Question : 72 of 100

Marks: +1, -0

△ A B C

is an equilateral triangle.

D

and

E

are points on

A B

and

A C

respectively such that

D E

is parallel to

B C

and is equal to half the length of

B C

. If

A D+C E+B C=30 {cm}

, then find the perimeter (in

{cm}

) of the quadrilateral

B C E D

.

$37.5$
25
45
35

Solution:

Given,

D E=\;{B C}/{2}

and

A D+C E+B C=30

\;A D=A E, A B=B C=A C

⇒\;A E+E C+B C=30

⇒\;A C+B C=30

⇒\;A C=B C=15=A B

\;\text " and "\;\;D E=\;{B C}/{2}=\;{15}/{2}=7.5 {cm}

Perimeter of

B C E D

\;\; =B C+C E+E D+D B

\;\; =15+7.5+7.5+7.5

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